A152220 Primes p such that p^2 divides m!-1 for some integer m < p.

11, 31, 107, 571, 971, 4931

Offset

1,1

Comments

For numbers k such that k! - 1 is divisible by a square see A152219.

a(7) > 60000, if it exists. - Amiram Eldar, Oct 23 2024

Links

Table of n, a(n) for n=1..6.

Mathematica

aa = {}; Do[If[(Sqrt[n! - 1] /. Sqrt[_] -> 1) > 1, Print[n]; AppendTo[aa, (Sqrt[n! - 1] /. Sqrt[_] -> 1)], {n, 1, 1000}]; aa
q[p_] := Module[{m = 2}, While[m < p && ! Divisible[m! - 1, p^2], m++]; Divisible[m! - 1, p^2]]; Select[Prime[Range[660]], q] (* Amiram Eldar, Oct 23 2024 *)

Prog

(PARI) is(p) = if(isprime(p), my(m = 2); while(m < p && (m! - 1) % (p^2), m++); !((m! - 1) % (p^2)), 0); \\ Amiram Eldar, Oct 23 2024

Crossrefs

Cf. A064237, A152219, A152231, A152232.

Sequence in context: A192246 A124296 A223388 * A272263 A082712 A049090

Adjacent sequences: A152217 A152218 A152219 * A152221 A152222 A152223

Keyword

nonn,more

Author

Artur Jasinski, Nov 29 2008

Extensions

a(6) from Artur Jasinski, Nov 30 2008

Status

approved